The formulæ of the special theory of relativity give us, correspondingly, for the amplitude in the moving system
According to Maxwell's theory the energy of the light-wave per unit volume is
. We now wish to calculate the corresponding energy-density also with respect to the moving system. We must here take into account that, in consequence of the contraction of the lengths according to the Lorentz-Einstein transformation formulæ, the volume
of a sphere in the resting system becomes transformed into that of am ellipsoid as measured from the moving system
; indeed, this volume of the ellipsoid is
